Latest Developments in Nonlinear Sciences

This paper outlines a detailed study of some latest trends and developments in nonlinear sciences. The major focus of our study will be variational iteration (VIM) and its modifications, homotopy perturbation (HPM), parameter expansion and exp-function methods. The above mentioned schemes are highly accurate, extraordinary efficient, capable to cope with the versatility of the physical problems and are being used to solve a wide class of nonlinear problems. Several examples are given which reveal the justification of our claim

Variational Iteration Method for Solving Initial and Boundary Value Problems of Bratu-type

In this paper, we present a reliable framework to solve the initial and boundary value problems of Bratu-type which are widely applicable in fuel ignition of the combustion theory and heat transfer. The algorithm rests mainly on a relatively new technique, the variational iteration method. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm

Exact solitary-wave Special Solutions for the Nonlinear Dispersive K(m,n) Equations by Means of the Homotopy Analysis Method

In this paper, we study the nonlinear dispersive K(m,n) equations which exhibit solutions with solitary patterns. New exact solitary solutions are found. The two special cases, K(2, 2) and K(3, 3), are chosen to illustrate the concrete features of the homotopy analysis method in K(m,n) equations. The nonlinear equations K(m,n) are studied for two different cases, namely when m = n being odd and even integers. General formulas for the solutions of K(m,n) equations are established

On the Solution of the Vibration Equation by Means of the Homotopy Perturbation Method

In this paper, we present a reliable algorithm, the homotopy perturbation method, to solve the well-known vibration equation for very large membrane which is given initial conditions. By using initial value, the explicit solutions of the equation for different cases have been derived, which accelerate the rapid convergence of the series solution. Numerical results show that the homotopy perturbation method is easy to implement and accurate when applied to differential equations. Numerical results for different particular cases of the problem are presented graphically

On Numerical Solutions of Two-Dimensional Boussinesq Equations by Using Adomian Decomposition and He\u27s Homotopy Perturbation Method

In this paper, we obtain the approximate solution for 2-dimensional Boussinesq equation with initial condition by Adomian\u27s decomposition and homotopy perturbation methods and numerical results are compared with exact solutions

Penerapanimetodeicapitaliassetipricingimodeli(capm) Sebagai Dasar Pengambilan Keputusan Investasi Saham (Studi Pada Perusahaan Yang Terdaftar Di Indeks Idx30 Periode Juli 2012-juni 2015)

This research aims to classify efficient shares and inefficient shares using CAPM method so investors are able to make a precise investment decision. CAPM method is used to assess the relation between risk and expected return of investment. The type of research is descriptive research with quantitative approach. The research population consists of 30 companies which had been listed on IDX30 in 2012-2015 and 15 companies among them are the research sample. The result showed that the majority of shares results a positive return for the research period and there are only 3 shares result a negative return. A stock with the lowest beta has the lowest expected return as well and a stock with the highest beta has the highest expected return too. That is proving that there is a positive and linear relationship between systematic risk and expected return. Besides, there are 9 efficient shares and 6 inefficient shares based on CAPM method. Efficient shares are undervalued shares (cheap) that have bigger individual return than its expected return [Ri>E(Ri)], while inefficient shares are shares with smaller individual return than its expected return [Ri<E(Ri)] and classified as overvalued shares (expensive)

Flavour-singlet g_A and the QCD sum rule incorporating instanton effects

We derive a QCD sum rule for the flavour-singlet axial coupling constant $g_A^{(0)}$ from a two point correlation function of flavour-singlet axial vector currents in a one-nucleon state. In evaluating the correlation function by an operator product expansion we take into account the terms up to dimension 6. This correlation function receives an additional two-loop diagram which comes from an (anti-)instanton. If we do not include it, $g_A^{(0)}$ is estimated to be 0.8. However, the additional diagram due to instantons contributes negatively and reduces $g_A^{(0)}$ towards the experimental value.Comment: 15 pages, 2 figure

Nisin inducible production of listeriolysin O in Lactococcus lactis NZ9000

<p>Abstract</p> <p>Background</p> <p><it>Listeria monocytogenes </it>is a well-characterized food-borne pathogen that infects pregnant women and immunocompromised individuals. Listeriolysin O (LLO) is the major virulence factor of the pathogen and is often used as a diagnostic marker for detection of <it>L. monocytogenes</it>. In addition, LLO represents a potent antigen driving T cell-mediated immunity during infection. In the present work, <it>Lactococcus lactis </it>NZ9000 was used as an expression host to hyper-produce LLO under inducible conditions using the NICE (NIsin Controlled Expression) system. We created a modified pNZ8048 vector encoding a six-His-tagged LLO downstream of the strong inducible PnisA promoter.</p> <p>Results</p> <p>The constructed vector (pNZPnisA:CYTO-LLO) was expressed in <it>L. lactis </it>NZ9000 and was best induced at mid-log phase with 0.2% v/v nisin for 4 h statically at 30°C. Purification of the His-tagged LLO was accomplished by Ni-NTA affinity chromatography and functionality was confirmed through haemolytic assays. Total LLO yield (measured as total protein content) was 4.43–5.9 mg per litre culture and the haemolytic activity was still detectable after 8 months of storage at 4°C.</p> <p>Conclusion</p> <p>The LLO production method described in this work provides an approach to efficient LLO production in the Gram-positive <it>Lactococcus </it>bacterium to yield a significant source of the protein for research and diagnostic applications. Expression of LLO in <it>L. lactis </it>has a number of benefits over <it>E. coli </it>which may facilitate both <it>in vivo </it>and <it>in vitro </it>applications of this system.</p